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Long Division Calculator with Remainders

Calculator Use

Divide two numbers, a dividend and a divisor, and find the answer as a quotient with a remainder. Learn how to solve long division with remainders, or practice your own long division problems and use this calculator to check your answers.

Long division with remainders is one of two methods of doing long division by hand. It is somewhat easier than solving a division problem by finding a quotient answer with a decimal. If you need to do long division with decimals use our Long Division with Decimals Calculator .

What Are the Parts of Division

For the division sentence 487 ÷ 32 = 15 R 7

• 487 is the dividend
• 32 is the divisor
• 15 is the quotient part of the answer
• 7 is the remainder part of the answer

How to do Long Division With Remainders

From the example above let's divide 487 by 32 showing the work.

Further Reading

At Ask Dr. Math you can find Instructions for Long Division for simple and more advanced long division problems.

Math is Fun also provides a step-by-step process for long division with Long Division with Remainders .

Cite this content, page or calculator as:

Furey, Edward " Long Division Calculator with Remainders " at https://www.calculatorsoup.com/calculators/math/longdivision.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: October 19, 2023

Long Division Calculator – with Steps to Solve

Enter the divisor and dividend below to calculate the quotient and remainder using long division. The results and steps to solve it are shown below.

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On this page:

• Long Division Calculator

How to Do Long Division with Remainders

Parts of a long division problem, steps to calculate a long division problem, how to get the quotient and remainder as a decimal, how to do long division without division, frequently asked questions.

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

Ethan has a PhD in astrophysics and is currently a satellite imaging scientist. He specializes in math, science, and astrophysics.

Learning long division is a crucial milestone in understanding essential math skills and a rite of passage to completing elementary school. It strikes fear in elementary school students and parents alike.

A recent study found that the understanding of long division and fractions in elementary school is directly linked to the student’s ability to learn and understand algebra later in school. [1]

Have no fear!

Learning long division can be easy, and in just a few easy steps, you can solve any long division problem. Follow along as we break it down, but first, we need to cover the anatomy of a long division problem.

There are a few parts to a long division problem, as shown in the image above.

The dividend is the number being divided and appears to the right and under the division line.

The divisor is the number being divided by and appears to the left of the division line.

The quotient is the solution and is shown above the dividend over the division line. Often in long division, the quotient is referred to as just the whole number part of the solution.

The remainder is the remaining part of the solution, or what’s leftover, that doesn’t fit evenly into the quotient.

There are a few main steps to solving a long division problem: divide, multiply, subtract, bringing the number down, and repeating the process.

Step One: Set up the Expression

The first step in solving a long division problem is to draw the equation that needs to be solved. If the problem is already in long division form, then skip along to step two.

If it’s not, this is how to draw the long division problem.

Start by drawing a vertical bar to separate the divisor and dividend and an overbar to separate the dividend and quotient.

Place the dividend to the right of the vertical bar and under the overbar. Place the divisor to the left of the vertical bar.

For example , to divide 75 by 4, the long division problem should look like this:

Step Two: Divide

With the long division problem drawn, start by dividing the first digit in the dividend by the divisor.

You can also think about this as counting the number of times the divisor will evenly fit into this digit in the dividend.

If the divisor does not fit into the first digit an even number of times, drop the remainder or decimal portion of the result and write the whole number portion of the result in the quotient above the overline directly above the digit in the dividend.

For example , the divisor “4” goes evenly into the first digit of the dividend “7” one time, so a “1” can be added to the quotient above the 7.

Step Three: Multiply

The next step is to multiply the divisor by the digit just added to the quotient. Write the result below the digit in the dividend.

This step forms the part of the expression for the next step.

Continuing with our example, multiplying the divisor “4” by “1”, which we found in the previous step, equals “4”. So, add a “4” below the first digit in the dividend.

Step Four: Subtract

Now, add a minus sign “-” before the number added in the previous step and draw a line below it to form a subtraction expression.

Continuing the example above, add a “-” before the “4” and a subtraction line below it.

Now that you have created a subtraction problem, it’s time to solve it.

To solve, subtract “7” minus “4”, which equals “3”, so write a “3” below the subtraction line.

Note: if the resulting value of the subtraction problem is greater than the divisor, then you made a mistake in step 2 and should double-check your work.

If the long division problem has a dividend that is a single digit, then hooray, you’re done! The remaining number that is the result of the subtraction problem is the remainder , and the number above the dividend is the whole number quotient.

If more digits are remaining in the dividend, then proceed to the next step.

Step Five: Pull Down the Next Number

At this point in the process, it’s time to operate on the next number in the dividend. To do this, pull down the next digit in the dividend and place it directly to the right of the result from the subtraction problem above.

The next digit in the dividend is “5”. So, pull “5” down and write it next to the “3” found in the previous step.

Step Six: Repeat

At this point, you might be wondering where to go from here. Repeat steps two to five until all the digits in the dividend have been pulled down, divided, multiplied, and subtracted.

When dividing, use the result of the subtraction problem combined with the pulled-down digit as the dividend and divide the divisor into it.

Continuing the examples above, divide the result of the subtraction problem and the pulled-down digit by the divisor. Thus, the next step is to divide 35 by 4. The result is “8”, so add “8” to the quotient.

Next, multiply the quotient digit “8” by the divisor “4”, which equals 32. Add “32” to the long division problem and place a negative sign in front of it.

Next, repeat the subtraction process, subtracting 32 from 35, which equals 3. Add a “3” below the subtraction line. Since there are no longer any remaining digits in the dividend, this is the remainder portion of the solution.

Therefore, 75 divided by 4 is 18 with a remainder of 3. As you practice these steps, use the calculator above to confirm your answer and validate your steps solving long division problems.

If you’ve gotten this far, then you should have a good idea of how to solve a long division problem, but you might be stuck if you need to get the quotient as a decimal rather than a whole number with a remainder.

To calculate the quotient in decimal form, follow the steps above the get the whole number and remainder.

Next, divide the remainder by the divisor to get the remainder as a decimal. Finally, add the decimal to the quotient to get the quotient in decimal form.

For example , 75 ÷ 4 is 18 with a remainder of 3.

Divide 3 by 4 to get the decimal 0.75. 3 ÷ 4 = 0.75

Then, add 0.75 to 18 to get the quotient as a decimal. 0.75 + 18 = 18.75

Thus, the decimal form of 75 ÷ 4 equals 18.75.

While it defeats the purpose of actually learning how to do long division, there is technically a way to perform long division without actually doing any division. The way to do this is as follows.

Set up the long division expression the exact same way as you would normally.

Step Two: Repeatedly Subtract the Divisor

Now, subtract the divisor from the dividend. Afterward, subtract the divisor again from the remaining value. Do this repeatedly until the remaining value is less than the divisor.

Step Three: Count the Number of Subtractions

Finally, to find the quotient, simply count the number of times you subtracted the divisor. This is the whole number portion of the quotient, and the final remaining value is the remainder.

Note: While this method of solving long division problems may seem easier, it is often very impractical to do so. For example, in the above example of 75 divided by 4, you would need to repeat the subtraction 18 times!

Therefore, traditional long division is the vastly superior method.

Why is long division important?

Long division is important not just because it is a tool that allows us to solve difficult division problems, but because it helps to teach logical thinking that will prepare students to excel in solving future mathematical problems.

Why do we still teach long division?

We still teach long division because it teaches students how to think logically, a valuable skill that is shown not just to improve future understanding of algebraic concepts, but also to help solve problems in all aspects of their lives.

How do you check a long division answer?

Just like subtraction is the opposite of addition, multiplication is the opposite of division. Therefore, to check a long division answer, multiply the quotient by the divisor, and if it equals the dividend, then the answer is correct!

Can you do long division on a calculator?

While a calculator can solve division problems, it will not list out the steps used in evaluating a long division problem, and will therefore not improve your understanding of how to perform long division.

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• Carnegie Mellon University, Press Release: Carnegie Mellon-Led Research Team Finds Knowledge Of Fractions and Long Division Predicts Long-Term Math Success, https://www.cmu.edu/news/stories/archives/2012/june/june15_mathsuccess.html

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Long Division Problems with Answers

(randomly generated).

Welcome to our Long Division Problems with Answers page.

Here you will find our free worksheet generator for generating your own long division sheets and answers.

If you are looking to create your own custom-made long or short division worksheets then look no further!

We also have several worked examples showing long division on this page so you can see how the method works.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

Using the random sheet generator will allow you to:

• choose the number range and number of questions you wish the worksheet to have;
• print or save your worksheet and a corresponding answer sheet;
• choose your own title and instructions for completing the sheet - great for homework!

For optimal printing, please set your margins to zero on your print setup options.

To save your worksheets, select Print to PDF in the printing options.

If you have any problems with our Random Generator, please let us know using the Contact Us link at the top of each page.

Mobile View of Worksheets

Please note that our generated worksheets may have problems displaying correctly on some mobile devices.

This should not affect the printing of the sheets which should display correctly.

Long Division Problems with Answers Generator

Here is our random worksheet generator for creating your own long or short division worksheets.

You can generate a range of long division worksheets ranging from 2 digit by 1 digit up to 5 digits by 2 digits.

Using this generator will let you create your own worksheets for:

• Dividing 2, 3, 4 and 5 digit numbers by a range of different numbers up to 99;
• Dividing numbers with or without a remainder;
• Choosing exactly which divisors you want to include;

One of the best features of this generator is that you can choose individual values for the divisors for the worksheets (between 2 and 15).

This means that:

• if you were introducing long division for the first time, you could choose just to divide 2 digit numbers by, say, 2, 3 and 5.
• if you wanted to introduce dividing by two digits but you wanted to divide 3 digit numbers by 11 and 12, you could do that also.
• to access this feature, go to the 'Select divisors from a list' option.

To start creating your sheet, choose an option from the Number values box below.

Parts of a Long Division Equation

The dividend is the number being divided.

The divisor is the number you are dividing by.

The quotient is the number of times the divisor goes into the dividend.

The remainder is what is left over from the dividend when the divisor has been taken away as many times as it can be without leading to a negative answer.

The remainder can be a whole number, but it can also be expressed as a fraction or decimal.

Long Division Problems with Answers Worksheet Generator

4 Steps to Your Worksheets...

• Choose your divisor value - this is the number you are dividing by
• Choose your dividend value - this is the number you are dividing
• Choose if you want to have remainders or not
• Choose the number of questions
• View your sheet
• Print your sheet (if you want to save a hard copy of your sheet, choose 'Save to PDF'.

(Optional) Give your worksheet a title.

(Optional) Write out any instructions to go at the top of the sheet.

Divisor Value:

Remainders:

Dividend value:

Number of Questions:

Your worksheet will appear below.

Examples of Long Division Problems with Answers

Here are some examples showing some long division problems with answers, along with commentary on each step.

Example 1) Work out 84 ÷ 3

So we are working out \[ 3 \enclose {longdiv} {84} \]

FIrst step is to work out 8 ÷ 3, which means we need to find how many groups of 3 make 8.

We can get 2 groups of 3 in 8, and 2 x 3 = 6 so this gives us: \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \end{array} \]

Next we subtract 6 from 8 to give us: \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 2 \end{array} \]

The next step is to bring down the 4 and put it next to the 2 \[ \begin {array}{l} \quad 2 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \end{array} \]

We now have to work out 24 ÷ 3, or how many groups of 3 make 24.

8 groups of 3 make 24. So this gives us: \[ \begin {array}{l} \quad 28 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \\ \quad \underline{24} \end{array} \]

Finally subtract 24 from 24 to give us an answer of 0. \[ \begin {array}{l} \quad 28 \\ 3 \enclose {longdiv} {84} \\ \quad \underline{6} \\ \quad 24 \\ \quad \underline{24} \\ \quad \; \; 0 \end{array} \]

There are no more digits to bring down and we have no remainders, so we have finished.

Answer: 84 ÷ 3 = 28

Example 2) Work out 347 ÷ 4

So we are working out \[ 4 \enclose {longdiv} {347} \]

FIrst step is to work out 3 ÷ 4, which means we need to find how many groups of 4 make 3.

There are 0 groups of 4 in 3, so we keep the 3 in its place and go on to the next digit which is 4.

This gives us: \[ \begin {array}{l} \quad 0 \\ 4 \enclose {longdiv} {347} \end{array} \]

So the next step is to work out 34 ÷ 4, or find how many groups of 4 make 34.

8 groups of 4 make 32. So this gives us: \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \end{array} \]

We subtract 32 from 34 to give us an answer of 2. This gives us: \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 2 \end{array} \]

Next we bring the 7 down alongside the 2. \[ \begin {array}{l} \quad 08 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \end{array} \]

So we need to work out 27 ÷ 4, or find how many 4s make 27.

6 groups of 4 make 24. So this gives us: \[ \begin {array}{l} \quad 086 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \\ \quad \; \; \underline {24} \end{array} \]

Finally we need to subtract 24 from 27 to give us 3.

There are no more digits to bring down, so we are left with 3 as a remainder. \[ \begin {array}{l} \quad 086r3 \\ 4 \enclose {longdiv} {347} \\ \quad \underline {32} \\ \quad \; \; 27 \\ \quad \; \; \underline {24} \\ \quad \quad 3 \end{array} \]

Answer: 347 ÷ 4 = 86r3

If we wanted the remainder as a fraction, we would have 347 ÷ 4 = 86 ¾

Example 3) Work out 8165 ÷ 12

So we are working out \[ 12 \enclose {longdiv} {8165} \]

FIrst step is to work out 8 ÷ 12, which means we need to find how many groups of 12 make 8.

There are 0 groups of 12 in 8, so we keep the 8 in its place and go on to the next digit which is 1.

This gives us: \[ \begin {array}{l} \quad \; 0 \\ 12 \enclose {longdiv} {8165} \end{array} \]

So the next step is to work out 81 ÷ 12, or find how many groups of 12 make 81.

6 groups of 12 make 72. So this gives us: \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \end{array} \]

6 groups of 12 make 72. So this gives us: \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 9 \end{array} \]

Next we bring the 6 down alongside the 9. \[ \begin {array}{l} \quad \; 06 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \end{array} \]

So we need to work out 96 ÷ 12, or find how many 12s make 96.

8 groups of 12 make 96. So this gives us: \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \end{array} \]

Now we subtract 96 from 96 to give us 0. \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 0 \end{array} \]

Now we bring down the 5. \[ \begin {array}{l} \quad \; 068 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \end{array} \]

Nexy we need to work out 5 ÷ 12, or how many 12s make 5.

0 groups of 12 make 5, so this gives us: \[ \begin {array}{l} \quad \; 0680 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \\ \qquad \; \: \underline {00} \end{array} \]

Subtracting 0 from 5 gives us 5. There are no more digits to bring down, so 5 is the remainder. \[ \begin {array}{l} \quad \; 0680r5 \\ 12 \enclose {longdiv} {8165} \\ \quad \; \, \underline {72} \\ \qquad 96 \\ \qquad \underline{96} \\ \qquad \; \: 05 \\ \qquad \; \: \underline {00} \\ \qquad \quad 5 \end{array} \]

Answer: 8165 ÷ 12 = 680r5

If we wanted the remainder as a fraction, we would have \[ 8165 \div 12 = 680 {5 \over 12} \]

Other Recommended Worksheets & Resources

Here are some of our other related worksheets you might want to look at.

Long Division Support

We have created a calculator to help you master the long division method.

Just type in the dividend and divisor and let the calculator show you how to work out the long division, step-by-step.

The calculator also gives commentary to show you what is happending at each stage.

• Step by Step Long Division Calculator

More Randomly Generated Multiplication and Division Worksheets

As well as our long division problems with answers generator on this page, we also have a a generator for making your own division facts and several multiplication worksheet generators.

• Long Division with Money (randomly generated)
• Division Facts Worksheet Generator
• Single Digit Multiplication Worksheets Generator
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Graded (non-generated) Division Sheets

As well as our randomly generated long division worksheets, we also have a selection of carefully graded division worksheets for each grade.

These sheets are especially useful for introducing the concept and keeping the numbers to divide manageable and simple.

The sheets in the links below are not randomly generated, but have been carefully selected to progress your child through their division learning.

Learning long division starts at a 3rd grade level with learning to divide by a single digit. It then gradually gets more complex for higher grades.

Long Division Worksheets (graded)

• Long Division Worksheets 3rd Grade
• 4th Grade Long Division Worksheets
• Long Division Worksheets 5th Grade
• Long Division of Decimal Numbers

Mental Division Worksheets

As well as long division worksheets, you also need to know your division facts.

Knowing your division facts will help improve the speed and accuracy of your long division.

We have a wide variety of division fact worksheets for you to choose from.

Division Facts Worksheets

Division facts starts off with understanding the link between multiplication and division.

Once you understand this, you can start learning the division facts related to the multiplication table.

After this, at a 4th and 5th grade level, you can start learning related division facts.

This means that if you know that 12 ÷ 4 = 3 then you can work out 120 ÷ 4 = 30 or that 120 ÷ 40 = 3, etc

• Understanding Division Sheets (2nd grade)
• Division Facts to 10x10 Worksheets (3rd grade)
• Divding by Multiples of 10 and 100 Worksheets (4th grade)
• Decimal Division Facts (5th grade)

Multiply and Divide by 10 and 100

Knowing how to multiply and divide numbers by 10 and 100 is a very useful skill.

It is especially useful when converting between metric units or when using percentages.

• Multiply and Divide by 10 and 100 (decimals)

Division Math Games

Here you will find a range of Free Division Games.

The following games develop the Math skill of dividing and learning your division facts in a fun and motivating way.

Using these sheets will help your child to:

• learn their division facts;
• develop their strategic thinking skills.
• Math Division Games

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Division in Math

Division is a math superpower that breaks down a whole — whether you’re cutting a pizza or divvying up some candy!

Author Christina Levandowski

Expert Reviewer Jill Padfield

Published: August 24, 2023

• Key takeaways
• Division is an opposite game – If you multiply numbers, you can “undo” them using division. It’s multiplication’s opposite function! 
• There’s a few signs to look for – There are three main symbols for division.
• You won’t always get “even Stevens” – Sometimes, you’ll have a little left over. That leftover number is known as the “remainder.”

Table of contents

What is division?

Common symbols and terminology, properties of division, how to divide in 6 easy steps, what is long division, working with remainders.

• Let’s practice together!

Practice problems

Division is one of the most important math skills you’ll practice, helping you to undo multiplication problems or break off parts of a “whole.” We know it looks complicated, but it really isn’t! You just need to know what signs to look for that tell you when division is needed. 

Like addition and subtraction, division uses a few special terms and symbols. Knowing these can help you to work out your problems quickly and correctly. 

We know it sounds complicated right now — but with a little practice and this handy guide, you’ll be flying through your math homework in no time!

Division is a process in math that lets you break down a number into multiple, equal parts. Sometimes, you can cut everything down into whole number parts, and, sometimes, you’ll be left with a little leftover, giving you a decimal or fraction for an answer rather than a whole number. 

You’ll often see division problems vertically, like this:

It can also be written horizontally: 10 ÷ 2, as 10/2 , or using a division bar: 2 ⟌ 10.

No matter how you see it, though, the use for it is always the same. You’re breaking down a number or quantity into smaller pieces. 

Let’s take a look at some key terms that’ll help you build your division skills.

Division is a simple mathematical operation, but there are still a few terms to know to help you find the correct solution. 

Here are the terms you need to know to solve division equations with ease:

➗ — This is known as a division sign, and it tells you that a number needs to be broken down into multiple pieces. 

⟌ — This is the division bar, and it also means to divide. On the outside of the bar, you’ll see the number determining how many pieces are needed from the whole (the divisor), and the dividend on the inside, which is what you’ll be dividing. The answer goes on the top of the bar. 

∕ — This is known as the division slash. Generally, the divisor comes first, and the dividend will appear second.

Important vocabulary

• Divisor – The divisor is the number that is determining how many pieces are needed from the whole. For example: in 15 ÷ 3, three would be the divisor. It’s also the number located outside of the bracket when you see a division bar.
• Dividend – The dividend is the number that’s being divided, and it’s found inside the division bar.
• Quotient – The quotient is your answer, which goes after the equals (=) sign or on the top of the division bar.
• Remainder – In some cases, you’ll have a remainder — which means that the divisor can’t be equally divided into the dividend. The remainder is written to the side of your equation next to the division bar.

Anytime you see the word “property” in math, know that it’s just a rule to remember as you work through your groups of problems. Here are some of the most important properties of division that you need to know: 

• The Division By 1 Property:  If a number is divided by 1, the quotient will always be the original number. 
• The Division By Itself Property: If a number is divided by itself, the quotient will always be 1. 
• The Division By 0 Property: If a number is divided by 0, it’s “undefined” and cannot be solved. 
• The Division Of 0 By (Any) Number Property: If a 0 value is divided by any number, you’ll have 0 as your quotient.

Knowing these helpful properties can help you to do basic operations (like division) confidently. Remember — these are division facts, so these properties will always be true…no matter what problem you’re working to find the quotient to!

Now that you know the terms and properties of your division operation, it’s time to practice your skills. Let’s work the problem below together. 

1. Prepare your equation

We know that the problem above can feel overwhelming — so we want to take this moment to remind you that what we’re doing is breaking down a number into smaller numbers (or smaller groups of numbers). 

First things first, we have to prepare the equation. Feel free to keep it horizontal,  write it vertically, or use a division bar if you’d like. Use whatever method you feel comfortable with. 

Remember: The dividend (15) belongs inside the division bar if you choose to use that method. 

2. Start with the first digit of the dividend from the left

As we begin to divide, we need to start from the first digit from the left (in this case, 1) and ask ourselves: Does the divisor (3) go into 1 at least once? 

The answer here is “no,” so we will then evaluate the first AND second integer (making 15) as a dividend. 

We ask again: Does the divisor (3) go into 15 at least once? 

Now, the answer is “yes” — we just have to count how many times 3 can go into 15, starting our division process.* 

*NOTE: You can do this by using basic arithmetic operations (such as multiplication) to “undo” the problem (i.e., 3 x ? = 15) or counting by threes until you reach 15. 

In our case, 3 goes into 15 a total of five times.

3. Divide it by the divisor and write the answer on top as the quotient

Now that we know that 15 ÷ 3 = 5, it’s time to write it into our equation. Go ahead and write 5 behind the equals sign or standing tall at the top of your division bar. 

4. Subtract the product of the divisor and the digit written in the quotient from the first digit of the dividend

Now, we have to check our work. We have to ask ourselves: What is 5 x 3? Does it equal our dividend? If it does, you’re golden — you’ve done it! 

Do the multiplication, and then subtract your product to ensure that there’s no other steps remaining (like you’d see in the case of a remainder). 

In our example, 15 – 15 = 0…so no remainder or further action is needed.

5. Bring down the next digit in the dividend (if possible)

In other problems, if you did have a three or four digit dividend, you might need to bring down the next digit in the dividend, and determine if your divisor divides that number cleanly. 

You would then repeat the division process, putting your answer over the third or “next” place above the division bar as part of the quotient. 

Next, yo would repeat step 4 to determine if more steps in the division process are needed.

In our example, we don’t have to do this, so we will leave it as is. Good work!

Congratulations! You just broke a large number down into equal, separate parts. It’s time to repeat the process for your other problems. 

Long division is a form of division that’s used to break down larger numbers and will generally repeat steps 1-6 above at least three or more times. 

We’ll work on that stuff later — for now, let’s just focus on mastering the basics!

What happens when you wind up with a little extra left over, you might ask? While it can look pretty scary, it’s simple to solve.

To do this, you’ll repeat steps one through five above until you get a number that cannot continue to be divided evenly. At this point, you’ll do a few additional steps:

• Determine how many times the divisor goes in to the product of your current answer and the divisor. This won’t be a clean number, and that’s OKAY — that’s what your remainder process is for.
• Complete the subtraction steps. After you get your number, complete the subtraction steps and write your answer below the subtraction bar.
• For example: In the case of 16 ➗ 3, we would write the quotient as: 5R1.

When you see that there’s zero left over, or if there is no way for the divisor to divide into the dividend, that means that your problem is solved!

Let’s practice together

• We ask: “How many times can 6 go into 2?” 
• 6 is greater than 2, so we will not be able to put a number over the 2. We then consider, “How many times can 6 go into 20?”
• Well, this is a bit of a challenge! 6 does not go into 20 evenly. 6 x 3= 18, and 6 x 4= 24. So, 6 can go into 20 three times, but it won’t go evenly.
• So, we add the 3 over the 0, above the division bar.
• We put the product of 6 x 3 (our divisor x our quotient) under the dividend and subtract to determine if the a remainder in our difference. 
• There is a remainder of 2. We write our quotient as: 3R2 .

• We know that our divisor is going to be 1, and our dividend (the number being divided) is 5. We identify them, and we put them properly into a division bar. 
• We ask: “How many times can 1 go into 5?” 
• Instead of working the problem counting or using multiplication, we remember the Division By 1 Property. 
• We put 5 at the top of our division bar, since any integer that is divided by 1 will always be itself. 
• There is no remainder for these types of Division By 1 Property problems. We can move on to the next problem.

• We know that our divisor is going to be 2, and our dividend (the number being divided) is 0. We identify them, and we put them properly into a division bar. 
• We ask, “How many times can 2 go into 0?” 
• Instead of working the problem counting or using multiplication, we remember the Division Of 0 By (Any) Number Property. 
• We put 0 at the top of our division bar, since any integer that attempts to divide 0 as a dividend will always result in a quotient of zero. 
• There is no remainder for these types of Division Of 0 By (Any) Number Property problems. We move on to the next problem.

Ready to give it a go?

You’ve done great so far — and you’re well on your way to mastering the art of division. Don’t be afraid to keep trying and make mistakes. 

Practice makes perfect, so we’ve given you a few more problems to practice as you work to perfect your skills. Remember: You can always scroll up to walk through the tutorials and refresh yourself on the terms, placement, and properties you’ll need to solve these correctly. 

By the end of this session, we’re confident that you’ll be ready to claim that A+ on your next math test. You can do it!

Click to reveal the answer.

The answer is 2 .

The answer is 1R6 .

The answer is 4 . 

Parent Guide

The answer is 2.

How did we get here? 

• We identify 4 as the dividend and 2 as the divisor, and place them in the division bar. 
• We ask: “How many times can 2 go into 4?” We determine this using the “count by twos” method, which shows us that 2 goes into 4 a total of two times. 
• We put 2 at the top of our division bar as the quotient, and multiply it by our divisor (2). We then subtract the product of our multiplication from the number to get an answer of 0, which shows us that there is no remainder. You’re done!

The answer is 1R6.

• We identify 8 as our divisor and 14 as our dividend, and place them in the division bar. 
• We ask: “How many times can 8 go into 14?”, as 8 will not go into 1. We determine this using the “count by eights” method, which shows us that 8 goes into 14 just once. 
• We write a 1 in the quotient place above the 4 under the division bar. We then multiply 1 x 8 to get a product of 8, which is placed below the 14 under the division bar. 
• Now, we do the math and subtract 8 from 14. We’ll get 6 as our difference. 
• We then write our quotient as 1R6.

The answer is 4. 

How did we get here?

• We identify 5 as our divisor and 20 as our dividend, and place them in the division bar. 
• We ask: “How many times can 5 go into 20,” as 5 will not go into 2 at all. We determine this using the “count by fives” method, which shows us that 5 can go into 20 cleanly four times. 
• We place a “4” in our quotient place, and multiply 4 x 5 to get a product of 20. This is written under the division bar as a subtraction problem. 
• We subtract 20 – 20, resulting in a difference of 0. 
• This means that 4 is our final quotient with no remainder.

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FAQs about math strategies for kids

We understand that diving into new information can sometimes be overwhelming, and questions often arise. That’s why we’ve meticulously crafted these FAQs, based on real questions from students and parents. We’ve got you covered!

Division is the mathematical process that breaks down a big value into smaller values. 

There are plenty of times you’ll use division in your everyday life. Some of the most common ways might be to break up an even quantity of something, determining how much of an ingredient to use, or grouping up items for use. 

Division is the inverse of multiplication. This means that it naturally undoes any sort of operation that’s done with multiplication. 

The three main parts of division are the divisor, dividend, and quotient. 

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Division Word Problems

Related Topics: More Lessons for Arithmetic Math Worksheets

Word problems with division often involve sharing from a total number. Take note which number is the dividend and which should be the divisor to solve the problem correctly.

Rosie has 60 sweets. If she gave her friends 3 sweets each, how many friends can she share her sweets with?

[60 sweets] ÷ [3 for each friend] 60 ÷ 3 = 20 friends

Dividing can also be seen as a number of times that one quantity can be taken from a total. Take note what the question is asking for – sometimes the question may ask for the remainder rather than the quotient.

Sam has $17. He wants to buy some hot dogs at $3 each. a) How many hot dogs can he buy? b) How much money would he have left?

[$17] ÷ [3 per hot dog] 17 ÷ 3 = 5 R 2 a) He can buy 5 hot dogs (Answer from the quotient) b) He would have $2 left (Answer from the remainder)

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Word Problems on Division

Word problems on division for fourth grade students are solved here step by step.

Consider the following examples on word problems involving division: 1. $5,876 are distributed equally among 26 men. How much money will each person get? Solution: Money received by 26 men = 5876 So, money received by one man = 5876 ÷ 26 = 226

Each man will get $226. 

2.  If 9975 kg of wheat is packed in 95 bags, how much wheat will each bag contain?

Since 95 bags contain wheat 9975 kg Therefore, 1 bag contains wheat (9975 ÷ 95) kg = 105 kg

Each bag contains wheat = 105 kg In a problem sum involving division, we have to be careful about using the remainder.

3. 89 people have been invited to a banquet. The caterer is arranging tables. Each table can seat 12 people. How many tables are needed? Solution: To answer this question, we need to divide 89 by 12 89 ÷ 12

Quotient -  7 

Remainder -  5

If the caterer arranges 7 tables, then 5 people will have no place to sit.  So he needs to arrange 7 + 1 = 8 tables. 

4.  How many hours are there in 1200 minutes? 

Solution: We know that there are 60 minutes in 1 hour.Divide the number of minutes by the number of minutes in 1 hour. We get, divide 1200 by 601200 ÷ 60 = 20

So there are 20 hours in 1200 minutes.

Answer: 20 hours. 

5. A bus can hold 108 passengers. If there are 12 rows of seats on the bus, how many seats are in each row? 

Solution: Total number of passengers = 108

There are 12 rows of seats on the bus.

To find how many seats are there in each row, divide the total number of passengers by the number of rows of seats on the bus.

We get, divide 108 by 12

108 ÷ 12 = 9

Therefore, there are 9 seats in each row.

Answer: 9 seats.

6. Tom had 63 apples. He divides all apples evenly among 9 friends. How many apples did Tom give to each of his friends?

Solution: Total number of apples = 63

There are 9 friends of seats on the bus.

To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends. 

We get, divide 63 by 9

Therefore, Tom gives 7 apples to each of his friends.

Answer: 7 Apples

7. Mark baked 195 cookies and divided them equally into 13 packs. How many cookies did Mark put in each packet?

Solution: Total number of cookies = 195

There are 13 packs.

To find how many cookies did Mark put in each packet, divide the total number of cookies by the number of packs.

We get, divide 195 by 13

195 ÷ 13 = 15

Therefore, Mark put 15 cookies in each pack.

Answer: 15 cookies.

9. Nancy needs 5 lemons to make a glass of orange juice. If Nancy has 250 oranges, how many glasses of orange juice can she make?

Solution: Total number of oranges = 250

She needs 5 lemons to make a glass of orange juice.

To find how many glasses of orange juice can Nancy make, divide the total number of oranges by the number of oranges needed for each glass of orange juice.

We get, divide 250 by 5

250 ÷ 5 = 50

Therefore, Nancy can make 50 glasses of orange juice.

Answer: 50 glasses of orange juice.

10. In your classes you counted 120 hands. How many students were at the class?

Solution: Total number of hands = 120

We have 2 hands.

To find how many students were at the class, divide the total number of hands by the number of hands we have.

We get, divide 120 by 2

220 ÷ 2 = 60

Therefore, there were 60 students at the class.

Answer: 60 students.

11. The total train fare for 20 persons is 7540 rupees. What is the fare for 1 person.

12. A milk container can store 8 litres of milk. How many containers are required to stare 6,408 litres of milk?

Capacity of one container = 8 lites of milk

Required number of containers = 6408 ÷  8

Hence, 801 containers are required.

13. A farmer produced 29800 kg of wheat. How many bags will be buy store the wheat if one bag can hold 70 kg?

Produced = 29890 kg

Number of bags needed = 29899 ÷  70

Therefore, 427 bags are needed to hold 29890 kg of wheat.

These are the basic word problems on division.

Questions and Answers on Word Problems on Division:

1. 92 bags of cement can be loaded in a truck. How many such trucks will be needed to load 2208 bags?

Answer: 24  trucks

2. The total train fare for 11 persons was $3850. What was the fare for one person?

Answer:  $350

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Long Division Calculator

Division is one of the basic arithmetic operations, the others being multiplication (the inverse of division), addition, and subtraction. The arithmetic operations are ways that numbers can be combined in order to make new numbers. Division can be thought of as the number of times a given number goes into another number. For example, 2 goes into 8 4 times, so 8 divided by 4 equals 2.

Division can be denoted in a few different ways. Using the example above:

8 ÷ 4 = 2

In order to more effectively discuss division, it is important to understand the different parts of a division problem.

Components of division

Generally, a division problem has three main parts: the dividend, divisor, and quotient. The number being divided is the dividend, the number that divides the dividend is the divisor, and the quotient is the result:

One way to think of the dividend is that it is the total number of objects available. The divisor is the desired number of groups of objects, and the quotient is the number of objects within each group. Thus, assuming that there are 8 people and the intent is to divide them into 4 groups, division indicates that each group would consist of 2 people. In this case, the number of people can be divided evenly between each group, but this is not always the case. There are two ways to divide numbers when the result won't be even. One way is to divide with a remainder, meaning that the division problem is carried out such that the quotient is an integer, and the leftover number is a remainder. For example, 9 cannot be evenly divided by 4. Instead, knowing that 8 ÷ 4 = 2, this can be used to determine that 9 ÷ 4 = 2 R1. In other words, 9 divided by 4 equals 2, with a remainder of 1. Long division can be used either to find a quotient with a remainder, or to find an exact decimal value.

How to perform long division?

To perform long division, first identify the dividend and divisor. To divide 100 by 7, where 100 is the dividend and 7 is the divisor, set up the long division problem by writing the dividend under a radicand, with the divisor to the left (divisorvdividend), then use the steps described below:

This is the stopping point if the goal is to find a quotient with a remainder. In this case, the quotient is 014 or 14, and the remainder is 2. Thus, the solution to the division problem is:

100 ÷ 7 = 14 R2

To continue the long division problem to find an exact value, continue the same process above, adding a decimal point after the quotient, and adding 0s to form new dividends until an exact solution is found, or until the quotient to a desired number of decimal places is determined.

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Division Word Problem Worksheets

This page contains extensive division word problems replete with engaging scenarios that involve two-digit and three-digit dividends and single digit divisors; three-digit dividends and two-digit divisors; and advanced division worksheets (four-digit and five-digit dividends). Thumb through some of these worksheets for free!

Division Word Problems for Beginners

These printable worksheets feature simple division word problems. The divisors are in the range 2 to 9. The quotients are in the range 2 to 10. These worksheets are building blocks for children.

• Download the set

Division: Two-digit by Single-digit (without Remainder)

This set of word problems involves dividing a two-digit number by a single-digit number to arrive at a quotient. The division leaves no remainder. Answer key is included in each worksheet.

Division: Two-digit by Single-digit (with Remainder)

These word problems require the learner to divide the two-digit dividend by the single-digit divisor and write down both the quotient and the remainder. Three pdf worksheets with 15 scenarios are featured here.

Theme based Word Problems

Each worksheet has five word problems related to the given theme. Supermarket, School and Halloween party are the themes used here.

Three-digit by Single-digit Word Problems

These printable worksheets involve division word problems with three-digit dividends and single digit divisors. Apply long division method to solve each problem.

Three-digit by Two-digit Word Problems

This set of word problems will require the student to perform division operations involving three-digit numbers and two-digit numbers. Verify your answer with the answer key provided in the worksheet.

Division: Four or Five-digit by Single-digit

Interesting scenarios are presented in these advanced worksheet pdfs that involve four-digit and five-digit dividends and single digit divisors. Use long division method to find the quotient.

Related Worksheets

» Addition Word Problems

» Subtraction Word Problems

» Multiplication Word Problems

» Word Problems

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Division Word Problems

• I have 80 matches and I will put 8 into each packet.
• There are two numbers in this question: 80 and 8.
• We identify the total number, which is 80.
• We identify the number in each group, which is 8.
• We divide the total by the number in each group to find the number of groups.
• 80 ÷ 8 = 10 and so, we can make 10 packets.

• Each shirt costs $11 and I have $66.
• We identify $66 as the total.
• $11 is the cost of each shirt.
• We want to know how many times 11 can go into 66.
• 66 ÷ 11 = 6 and so, 11 goes into 66 six times.
• We can spend $11 six times.

• Division by Sharing Equally
• Multiplication Word Problems

Simple Division Word Problems: Interactive Questions

Simple division word problems decimals worksheets and answers.

How to Identify Division Word Problems

Simple division word problems.

• Identify the numbers given in the question.
• Identify which number is the total quantity.
• Identify how many groups we are sharing between or how many need to go in each group.
• Divide the total by the number of groups to find the amount in each group.
• Or divide the total by how many needed in each group to find out how many groups can be made.

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Problem Solving on Division | Division Word Problems Examples with Answers

Are you looking for help in solving the division problems? If yes, then you are on the correct page. This Problem Solving on Division page includes the questions prepared by math experts. Students can check the detailed process to solve all those problems in the following sections. We know that division is an arithmetic operation that is inverse of multiplication and used to split the number of items into groups of equal size.

We are providing example questions and solutions for the various division problems. Interested students can solve the practice questions related to division to become a pro in the concept. All the Questions covered clearly explain how to solve problems involving division.

• Worksheet on Division Problems by 2-Digit Divisors
• Word Problems on Division by 2 Digit Number
• Word Problems on Division

Division Problem Solving Examples

Example 2: At a parking slot, we have 52 bikes in 4 rows. Find the number of bikes in each row? Solution: The total number of bikes = 52 The number of rows = 4 The number of bikes in each row = 52 ÷ 4 = 13 Therefore, the number of bikes in each row is 13.

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Divide Questions

Divide questions are essential to practice for the improvement of arithmetic skills in lower standards. The questions presented here will be beneficial for students to enhance their numeracy skills.

Also, check out What is Arithmetics ?

Division is an arithmetic operation that simply means “share equally”, “divide among”, “split into”, etc. For example, a pizza with 6 slices has to be equally distributed among three friends; then, obviously, one may say that each of them will get 2 slices of pizza. So, what we did here in terms of arithmetics is divide 6 by 3, which results in 2.

So, whenever we encounter problems that indicate a sense of sharing, dividing, distributing, etc. We must understand that the problem is related to division.

Learn more about divide .

Divide Questions with Solutions

Below are some divide questions and their solutions to help students understand different concepts regarding division.

Question 1:

What will be the quotient if 2468 is divided by 4?

Using the long division method,

Therefore, 2468 ÷ 4 = 617 or 2468 = 4 × 617.

Also, check: Long Division Online Calculator .

Question 2:

What number should be subtracted from 367 to make it divisible by 3?

Now, 367 = 3 × 122 + 1.

Hence, when 367 is divided by 3, it leaves a remainder of 1.

Thus, 367 – 1 = 366 is divisible by 3.

Question 3:

A shirt can be made out of 3 m cloth. If there is a roll of 1350 m cloth, how many total shirts can be made out of it?

Cloth needed to make a shirt = 3 m

Total cloth = 1350 m

Number of shirts = Total cloth ÷ cloth needed to make one shirt = 1350 ÷ 3 = 450.

Therefore, 450 shirts can be made.

Question 4:

What is the greatest number which can divide 24, 56 and 18?

The prime factorisation of 24, 56 and 28 are

24 = 2 × 2 × 2 × 3

56 = 2 × 2 × 2 × 7

28 = 2 × 2 × 7

We see that 2 × 2 = 4 is a common factor. Thus, 4 is the greatest number which can divide 24, 56 and 18.

Question 5:

Evaluate 2 + 24 × ½ ÷ ⅖.

The given problem can written as [2 + {24 × (½ ÷ ⅖)}]

= [2 + {24 × (½ × 5/2)}]

= [2 + {24 × 5/4}]

= [2 + {6 × 5}]

= 2 + 30 = 32

Question 6:

Evaluate 685/100.

Since there are 2 zeros in 100, we shall place the decimal point after two places counting from the ones place.

685/100 = 6.85.

Question 7:

Five friends went to a restaurant. The total bill was ₹ 2500. In what way they should split the bill so that each of them has to pay an equal amount?

Total amount = ₹ 2500

Number of person = 5

Amount each one has to pay = ₹ 2500/5 = ₹ 500.

Question 8:

What is the remainder when 2765 is divided by 6?

We see that 6 × 460 = 2760 and 6 × 461 = 2766

∴ 2765 = 6 × 460 + 5

Thus, 6 divides 2765 leaving a remainder of 5.

Question 9:

The cost of a per night stay at a hotel is ₹785. When checking out from the hotel, a man pays an amount of ₹3140. How many nights did he stay at the hotel?

Cost of one night at hotel = ₹785

Total amount paid = ₹3140

Number of nights = 3140/785 = 4

Therefore, he stayed for 4 nights at the hotel.

Question 10:

Divide 2.25 by 0.005.

2.25/0.005 = 225000/500 = 2250/5 = 450.

Video Lesson on How to Divide Numbers

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Practice Questions

1. Divide 2738 by 12.

2. The capacity of a glass is 300 ml. How many such glasses can be filled from 6 litres bottle of water?

3. What will be the remainder when 56846 is divided 4.

4. What is the greatest common number which can divide 240, 225 and 65?

5. Evaluate 29812/100.

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5 Fun Division Word Problems | Practice Multiple Ways of Solving | Free Printable

Division word problems.

Are your children ready to conquer division? These interactive, division problem-solving worksheets will help children solve division word problems in five different ways.

Division Problems

He has done it numerous times. Sharing a group of toys with his siblings, or even sharing a bag of M&M’s. In those situations, he instinctively knows how to do division problems.

When we hit the division problem in his math book, he wasn’t quite as sure what to do.

I wanted this little man of mine to be able to relate division to what he has done over and over while creating strategies for solving division problems.

These word problems with five steps were what we came up with. These simple division worksheets are perfect for 3rd grade division word problems.

How to Solve Division Word Problems

Step 1: division word problem solving by grouping.

The first step is the way we normally teach children to solve division problems. The students grab the amounts of objects that need to be divided up and then place them in the correct amount of groups. It is very hands-on and a visual way for our children to understand what is happening when we are dividing .

Step 2: Solving Division Word Problems by Repeated Subtraction

To solve a word problem using repeated subtraction, students start with the number being divided up or the dividend. Now they subtract the divisor or the number that tells how many groups are needed from the dividend over and over until they reach zero. The number of times they subtracted is the answer.

Step 3: Division Word Problem Solving with Arrays

Chances are if you taught multiplication in a hands-on way, you taught it using arrays. You can create an array when you place objects, pictures, or numbers in equal columns and equal rows.

With multiplication, you would take a problem like 4 x 5, and make 4 rows with 5 in each column. You would end up with 20 objects, which of course is the answer to the multiplication problem.

Division is a little different. If the problem is 18 ÷ 3, The student creates three rows. They then keep placing one object in each row until they have used 18 objects.

They now have an array that is a 3 by 6. The answer to the division problem is 6.

Want to know how to use arrays to divide when the numbers are larger? Check out this POST !

Step 4: Number Line to Solve Division Word Problems

Number lines have become an important tool in helping children solve problems. The beginning of this video by Ramy Melhem  clearly shows how to divide using a number line, and the little frog hopping is a great visual for our little ones.

Step 5: Create an Equation

The final step is very easy after all the work above. The students simply figure out what number was divided up, and place it in the first box.

They then look at how many groups they created, and that is the number that goes into the second box. Finally, they figure out how many objects were in each group and that is the answer or quotient.

That number goes in the last box.

By throwing in markers and painting with q-tips these sheets were fun for my little man, and I could see his understanding of division grow.

We moved on to these cut-and-paste division assessments, and his thinking was challenged even more. Through all this practice he is on his way to mastering simple division problems, and your kiddos can master it too.

Get This Cut and Paste Division Assessment at my TpT Store .

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Division Word Problems Printable

These free division math problems will help your students learn how to solve division problems 5 different ways. You can download this printable by clicking on the download button.

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25 Division Word Problems for Grades 3 to 5 With Tips On Supporting Students’ Progress

Steven eastes.

Division word problems are important in building proficiency in division. Division is one of the bedrocks of math alongside addition, subtraction and multiplication. Therefore, it is vital that students have a deep understanding of division, its function within arithmetic and word problems, and how to apply both short division and long division with success.

Division itself is the mathematical process of breaking a number up into equal parts and then finding out how many equal parts you can have. It may be that you have a remainder following the division or you may have no remainder and so a whole number as your answer.

What are division word problems?

Introducing standard algorithm division.

• Why are word problems important for childrens’ understanding of division?

Applying math to real life situations

Building problem solving skills, developing mathematical language skills, deepening understanding of the inverse relationship between division and multiplication, how to teach division word problem solving in elementary school., example of a division word problem, how can we show this visually, examples of division word problems in the elementary setting, 3rd grade division word problems, 4th grade division word problems, 5th grade division word problems.

Division word problems are an extension of the arithmetic method whereby they are word problems with division at the heart. Students will be expected to use the process of division to find a solution to the word problem.

Typically, word problems use a story as a scenario and are based on a real life situation where students are expected to interpret what the word problem is asking and then apply their division knowledge to find the answer. Division can also be introduced early through the idea of grouping before advancing to the formal method of long division.

To help you with the division journey, we have put together a collection of division word problems which can be used for children between 3rd grade to 5th grade.

Word Problems Grade 4 Fractions and Decimals

11 grade 4 fractions and decimals questions to develop reasoning and problem solving skills.

Division word problems in upper elementary

As children enter 3rd grade, they begin to develop their mental and written strategies for division. Students will begin to use their multiplication knowledge and times tables to assist in their solving of division problems and how they can use the corresponding division facts and multiplication facts to answer questions. 

By the end of 3rd grade, students are expected to recall their multiplication and division facts for multiplication times tables up to 10 x 10. They should also use their knowledge of place value, and known and derived facts to assist with simple division such as dividing by 1 and halving.

Introducing partial quotients 

Before being introduced to the standard algorithm, also known as long division, students learn the partial quotients method. Students practice their fluency of short division, in order to answer division word problems that have a whole number answer, and those with a remainder.

Before entering 4th and 5th grade, students encounter division word problems and multi step problems with increasingly harder numbers going from a simple division problem, such as, ‘If we have 30 students in our class and we are divided into groups of 5, how many students will be in each group?’ to ‘If there are 56 books in our library and they are shared among 7 children, how many books would each child get?

As our students enter 5th grade, the standard algorithm, or long division, is introduced. By the end of 5th grade, students should be fluent in both multiplication and division and the written strategies, and be able to apply knowledge in fraction word problems .

4th grade students work towards being able to divide up to 4 digit numbers by a one digit number using partial quotients and being able to interpret remainders in the correct context – even presenting the remainder as a decimal or fraction. Students should also be able to divide mentally and know how to divide by 10, 100 and 1,000 and how place value works alongside dividing a number so it is 10, 100 or 1,000 times smaller.

5th grade students are expected to consolidate on the above formal methods of division before being able to divide a four digit number by a two digit number using the formal method of standard algorithm division and to again be able to understand remainders within this and present them in the correct context. 

This also flows into division word problems as children should be able to read a multi step problem and know how to correctly interpret it, apply their divisional knowledge and solve the problem successfully. The concept of multi step problems is built upon at each stage of your state math curriculum.

Why are word problems important for childrens’ understanding of division?

Word problems, alongside the use of concrete objects and visual representations, are important in helping children understand the complexities and possible abstract nature of division.

While children may understand that when we divide our answer will be smaller, before providing a child with word problem worksheets, just like with exploring arrays to support multiplication word problems , it is important to visually explore how division looks – from grouping and beyond.

Word problems are important because they provide a real life context for children to understand division and how we encounter it in real life. By allowing children to see how division is used in everyday situations, children will find it more meaningful and relevant which in turn develops a deeper understanding of the four operations as a whole.

Word problems are also vital to developing problem solving skills. First, they must read and understand the problem before being able to identify the relevant information within the contextual problem and apply their knowledge to find a solution. This naturally builds critical thinking and a child’s ability to reason, which is an important skill for any mathematician.

Finally, the importance of  moving from simple division word problems to more challenging ones enhances students’ vocabulary and language skills. For children to develop an understanding of vocabulary such as divisors, quotient and remainders means they must first understand these key words and apply it to the process of division and be able to communicate clearly what they are aiming to do.

Division word problems also solidify the connection between multiplication and division. Understanding these inverse operations and being able to interchange the skills of multiplication and division will help make connections between different mathematical concepts and deepen students’ learning. 

Having taught the concept of division to students using concrete examples, for example how to group or share counters and cubes, the next step is to advance to division word problems. 

As with all word problems, it is important that students are able to read the question carefully and interpret it so they know what they are being asked. Do they need to add, subtract, multiply or divide? Are they solving a multi step problem and need to do more than one step? They may decide what operation to do, in this blogs’ case – division, and then choose to represent it visually.

There are 40 pieces of candy ready to go in the party bags for Laura’s birthday. They are to be shared between 8 friends. How many pieces of candy will each child get?

How to solve this:

First, we need to interpret the question. Laura has invited 8 friends to her party and she has 40 pieces of candy to share equally between her friends. So we know:

• There are 40 pieces of candy in total
• They are to be divided among 8 friends in total
• We will need to divide the total number of candies (40) by the number of friends (8). To solve this problem we could put the total number of candies (the dividend – 40 ) using the partial quotient method and divide by the total number of friends (the divisor – 8). If we do this, we would get the answer of 5 – the quotient. Each friend would get 5 pieces of candy each as 40 divided by 8 is 5.
• Alternatively, we could use the inverse – multiplication – to solve this problem. We may not know the division fact that 40 divided by 8 = 5 but if we look to the inverse we may know what number multiplied by 8 equals 40. If we did our 8 times table we would get the answer of 5 – the correct answer.

We could show 8 circles – each circle to represent a child – and place a piece of candy in each circle until we have placed all 40 candies. This would mean we have shared the candies equally between the friends and would result in each child having 5 candies.

We could represent the division word problem as a bar model. We could split the bar model into 8 sections. There are 40 candies and so we share them between the 8 sections. We will see that each section will get 5 pieces of candy.

The below visuals show how this would look:

Word problems are an important aspect of our learning at Third Space Learning’s one-to-one tutoring program. Tutors will work with our tutees to break down the word problems and identify the correct operation needed to solve the word problem.

Below are examples of what can be expected at each year group from grades 3 to 5. Through our tutoring program at Third Space Learning, our tutees will become familiar with word problems throughout their learning. They will encounter word problems on a regular basis with each lesson personalized to develop the learning our tutees need. The word problems will increase their confidence, familiarity with vocabulary and mathematical understanding.

Division word problems are essential to developing problem solving skills and mathematical reasoning.

Word problems for 3rd grade, students should begin using their recall of the times table facts they have learned to help with division word problems and be able to divide two digit numbers by one digit numbers using mental and partial quotients. Word problems may also involve multi step problems.

Question 1:

If a school has 90 students in 2nd grade and there are 3 classes in 2nd grade, how many students are in each class?

90 shared equally into 3 classes = 30 children per class

Question 2:

Every day a school gets a delivery of milk in a crate. There are 96 cartons of milk in the crate. If there are 8 milk cartons in a pack, how many packs will be in the crate?

96 divided by 12 = 8.

There are 8 cartons of milk in a pack.

Question 3:

A delivery of 96 footballs arrives at school for sports day. They are to be shared equally between 4 classes. How many footballs does each class get?

96 divided by 4 = 24 footballs per class

Question 4:

3rd grade is going to the beach on a school trip. If there are 100 children in 3rd grade and only 10 children can go on one mini bus, how many mini buses does Mr. Pearson need to book?

100 children divided 10 = 10 mini buses.

Question 5:

If you have 60 flowers and divide them into four flower pots, how many flowers are in each pot? Are there any left over?

Answer: 15 flowers in each pot.

If we divide 60 into 4 equal groups then we can use the partial quotient method.

When using the partial quotients method, students rely on what multiplication facts they can use. 

Because we are dividing 60 by 4, we may ask ourselves, what number can I multiply 4 by, to get close to 60 without going over? Students should be familiar with their 10s time tables, and 4 x 10 = 40. We place the 10 above the quotient line, and then subtract 40 from 60, leaving 20 remaining.

We will now start the process all over again. What number can I multiply 4 by to get close to 20 without going over? We know that 4 x 5 = 20, so again, place 5 above the 10 in the quotient line and subtract 20 – 20. Because there is nothing left over, we are done dividing.

So the answer to 60 divided by 4 = 15.

This would look like:

Word problems for 4th grade center around dividing a 4 digit number by a 1 digit number using the partial products method or area model method of division. They will also be introduced to remainders and be expected to interpret remainders correctly depending on the context. 

Ronan has a ball of string that is 819 cm long. He cuts it into 7 equal pieces. How long is 1 piece of string?

Answer: 117cm

819 divided by 7 = 117

In upper elementary there are 1,248 colored pencils. If there are 6 classes in upper elementary, how many pencils would each class receive?

Answer: 208

We use the division method to divide 1,248 by 6 and we get 208 as the result.

Mia buys three computer games for $84. How much is one computer game?

Answer: $28.

We divide $84.00 by 3 and we get $28.00.

The area of the school hall is 1,704m and needs to be split into four quadrants. What would be the area of each quadrant?

Answer: 426m

We take the total area of the school and divide it by 4 to represent each quadrant. In doing so, we would have 426m for each quadrant.

To check this is the correct answer, we could do the inverse and multiply 426 by 4 and we would get 1,704m.

Packets of candy are put into multi packs of 4. Today, 7,800 packets of candy were packed. How many boxes of candy were packed?

Answer: 163 boxes

We then have to take the total packets of candy– 7,800 – and divide this by 4. If we do this we will get the answer 1,950 boxes were packed.

Word problems for 5th grade will be preparing for the end of elementary school. They would be familiar with the concept of standard algorithm division and needing to divide a 4 digit number by a 2 digit number using the formal method of standard algorithm division.

A school is selling tickets at $6 each to attend the Big Christmas Fair. Over 15 weeks it has earned an amazing $9,720! On average, how many tickets were sold each week?

Answer: 108 tickets per week

First, we need to use the formal method of standard algorithm division to divide the grand total – $9,720 by 15. If we do this correctly we will have the answer 648.

Then, we need to take this answer of 648, which is how much is earned each week, and then divide this by $6, the amount each ticket is.

This will result in the number of tickets sold each week – 108 tickets.

A square sports field has a perimeter of 2.696km. How long is each side of the field?

Answer: 674m

To answer this we need to be able to convert the 2.696km into meters. There are 1000 meters in a kilometer so that would be 2,696m. Then we divide this by 4 and get 674m for one side.

Keira is given a toy blocks kit containing 2,208 individual blocks. She wants to split the toy blocks evenly between 15 friends and herself to work on making a toy block city together. How many blocks should she give each of her friends?

Answer: 138 blocks

We need to use the formal method of standard algorithm division to solve this. We also need to ensure we include Keira and her 15 friends so we have the number 16 as the divisor.

When we divide 2,208 by 16 using long division we get the answer 138.

Wesleigh was running in the cross country race. He ran for a distance of 3,569m and it took him 11 minutes to complete the race. How many meters did he run per minute? Give your answer to the nearest whole meter.

Answer: 324 meters

We need to use standard algorithm division to divide 3,569 by 11. That will give us an answer of 324.45. As the decimal can be rounded down, the answer is 324 meters.

Sophia is preparing her candy stall for the fair. She can fit 18 tins of candy into one crate. How many crates will be needed to fit 153 tins of candy?

Answer: 9 crates 

We divide 153 by 18 using standard algorithm division and we have an answer of 8, remainder 5. Therefore, having 8 crates would not be enough as we would have 85 tins left over and so we need a further tin to house the 5 tins left over. So, 9 crates are needed.

More word problems resources

Are you looking for more word problems resources? Take a look at our library of word problems practice questions including: time word problems , ratio word problems , addition word problems and subtraction word problems .

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by former Deputy Headteacher Steven Eastes and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.

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Solving Problems on Division Worksheet

Put your skills to the test by practicing to solve problems on division..

Know more about Solving Problems on Division Worksheet

Struggles with division can easily be overcome if students practice the concept in a fun and engaging way! Young learners will make connections between math and the real world as they solve a set of division word problems involving divide by scenarios. In these problems, they comprehend the scenarios and get to the result. This set of problems deals with numbers within 100.

Your one stop solution for all grade learning needs.

Division Problems Worksheets

Division problems worksheets give kids an idea of how to use the basic arithmetic operation division and apply it to different types of numbers. The problems range from simple divide the digits questions to tougher word problem sums.

Benefits of Division Problems Worksheets

Division forms one of the foundational pillars of Mathematics. It is not only used in solving textbook questions but also, to solve many real life problems. Hence, kids need to be well versed in the topic by practicing the sums in the division problems worksheets.

The division problems worksheets provide flexibility to kids so that they can work at their own pace without feeling pressured. They are also equipped with fun graphics that help kids to understand the topic in a better manner.

Download Division Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

☛ Check Grade wise Division Worksheets

• Division Worksheets for 1st Grade
• 2nd Grade Division Worksheets
• Division Worksheets for Grade 3
• 4th Grade Division Worksheets
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• Grade 8 Division Worksheets

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Division and Multiplication Problems with Solutions

•  / 

A firm foundation in multiplication and division is important for your child to succeed in advanced math. If your child is struggling, you might try creating practice problems for him or her to complete at home.

What Kinds of Division and Multiplication Problems Will My Child Encounter?

Multiplication and division typically are introduced in third grade. Students generally start their studies by memorizing multiplication and division facts for 0-12 and taking timed tests. You can help your child understand the relationship between multiplication and division by encouraging him or her to check work using the opposite operation. For example, your child can check his or her answer to the division problem 42 ÷ 6 = 7 by using multiplication: 6 x 7 = 42.

Also in elementary school, your child will learn long division, which typically involves larger numbers and, when numbers don't evenly divide, remainders. For example, in the problem 50 ÷ 12, the answer is four with a remainder of two (4 R2) because 12 x 4 = 48.

Your elementary student also will learn to multiply and divide fractions. With multiplication, the top numbers in the fractions, called the numerators, are multiplied together, as are the bottom numbers in the fractions, called the denominators. For instance, 3/4 x 1/5 = (3 x 1)/(4 x 5) = 3/20.

Dividing fractions is a bit more complicated because it involves inverting the second fraction. For example, with the problem 1/4 ÷ 6/2, you would flip the second fraction (6/2 becomes 2/6) and then multiply: 1/4 x 2/6 = 2/24, which can be reduced to 1/12.

Problems and Solutions by Concept

Basic multiplication and division.

1. Kennedy bought three shirts for $11 each. How much money did she spend?

2. Max has 15 cookies and five friends. How many cookies can he give to each friend?

Long Division

1. 202 ÷ 4

2. Karen has 108 inches of ribbon. For each present, she needs 18 inches of ribbon. How many presents can she decorate?

1. 8/7 x 3/1

2. 6/8 ÷ 4/5

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Division can be confusing, especially when working with larger numbers. Read on to learn how to help your fifth grader remember how to divide many different lengths of numbers.

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Inside Donald Trump’s secret, long-shot plan to end the war in Ukraine

Foreign policy experts and some republicans warned that pressuring ukraine to cede land would reward putin.

Former president Donald Trump has privately said he could end Russia’s war in Ukraine by pressuring Ukraine to give up some territory, according to people familiar with the plan. Some foreign policy experts said Trump’s idea would reward Russian President Vladimir Putin and condone the violation of internationally recognized borders by force.

Trump’s proposal consists of pushing Ukraine to cede Crimea and the Donbas border region to Russia, according to people who discussed it with Trump or his advisers and spoke on the condition of anonymity because those conversations were confidential. That approach, which has not been previously reported, would dramatically reverse President Biden’s policy, which has emphasized curtailing Russian aggression and providing military aid to Ukraine.

As he seeks a return to power, the presumptive Republican nominee has frequently boasted that he could negotiate a peace deal between Russia and Ukraine within 24 hours if elected, even before taking office. But he has repeatedly declined to specify publicly how he would quickly settle a war that has raged for more than two years and killed tens of thousands of soldiers and civilians.

Trump-aligned foreign-policy thinkers have emphasized addressing threats to U.S. interests from China and seeking ways to reverse Russia’s increasing dependence on China for military, industrial and economic assistance. They have also embraced limiting NATO expansion.

Privately, Trump has said that he thinks both Russia and Ukraine “want to save face, they want a way out,” and that people in parts of Ukraine would be okay with being part of Russia, according to a person who has discussed the matter directly with Trump.

Accepting Russian control over parts of Ukraine would expand the reach of Putin’s dictatorship after what has been the biggest land war in Europe since World War II. Some of Trump’s supporters have been trying to persuade him against such an outcome.

“I’ve been spending 100 percent of my time talking to Trump about Ukraine,” said Sen. Lindsey Graham (R-S.C.), a onetime Trump critic turned ally. “He has to pay a price. He can’t win at the end of this,” Graham added, speaking of Putin.

Russia has previously declared it was annexing Ukrainian land beyond the Donbas region and Crimea, and Ukraine’s president, Volodymyr Zelensky, has said he would not accept surrendering any territory. Exchanging territory for a cease-fire would put Ukraine in a worse position without assurances that Russia would not rearm and resume hostilities, as it has in the past, said Emma Ashford, a senior fellow at the Stimson Center, a nonpartisan think tank. “That is a terrible deal,” she said of Trump’s proposal.

The Trump campaign declined to directly address questions for this article. “Any speculation about President Trump’s plan is coming from unnamed and uninformed sources who have no idea what is going on or what will happen,” campaign spokeswoman Karoline Leavitt said in a statement. “President Trump is the only one talking about stopping the killing.”

Biden said in his State of the Union address that Putin is “on the march, invading Ukraine and sowing chaos throughout Europe and beyond,” and that Ukraine is trying to defend itself. The president has outlined a long-term plan of support for Ukraine that would build up its military capabilities this year so that it is in a better place to go on the offensive next year. But U.S. aid is already in jeopardy as House Speaker Mike Johnson (R-La.) faces a revolt from Republican hard-liners who are digging in against any more funding and clamoring to oust him.

Out of office, Trump has pressured congressional Republicans to resist additional U.S. support for Ukraine’s war effort and a return to the White House would significantly expand his influence over the debate. Seeing the political dynamics in the United States, European allies have jump-started military industry to a point where they hope to supplant a significant portion of the current U.S. assistance to Kyiv. But analysts said that realistically, Ukraine’s capacity to keep fighting would be weakened if Trump succeeds in blocking further U.S. aid.

In many ways, Trump’s plan is in line with his approach as president. His preference for splashy summits over policy details, confidence in his own negotiating skills and impatience with conventional diplomatic protocols were all hallmarks of how he approached foreign affairs in his first term.

In his eight years as the GOP’s standard-bearer, Trump has led a stark shift in the party’s prevailing orientation to become more skeptical of foreign intervention such as military aid to Ukraine. Trump has consistently complimented Putin, expressed admiration for his dictatorial rule and gone out of his way to avoid criticizing him, most recently for the death in jail of political opponent Alexei Navalny. He has not called for the release of Evan Gershkovich, the Wall Street Journal reporter held in Russia for a year without charges or a trial.

Trump has refused to acknowledge Russia’s interference in the 2016 election and falsely blamed Ukraine for trying to help Democratic rival Hillary Clinton — a smear spread by Russian spy services. His attempt in 2019 to withhold aid to Ukraine unless Zelensky announced an investigation into Biden led to Trump’s first impeachment.

In a phone call with Zelensky that year that Trump said was “perfect,” the U.S. president pressured Zelensky to investigate Biden and the discredited theory that Ukraine and not Russia sought to interfere with the 2016 election. The GOP-controlled Senate later acquitted Trump.

“Former president Trump’s inexplicable and admiring relationship with Putin, along with his unprecedented hostility to NATO, cannot give Europe or Ukraine any confidence in his dealings with Russia,” said Tom Donilon, President Barack Obama’s national security adviser. “Trump’s comments encouraging Russia to do whatever it wants with our European allies are among the most unsettling and dangerous statements made by a major party candidate for president. His position represents a clear and present danger to U.S. and European security.”

Graham said he has warned against giving Russia desired land and wants Trump to embrace a pathway forward for Ukraine to join NATO.

“The way you end this war to me is you make sure Ukraine gets into NATO and the E.U.,” he said. “He doesn’t say much about that. I don’t know if he’s thought too much about it.”

In his public promises to end the war, Trump has pointedly withheld the specifics on how he would negotiate with Putin and Zelensky. “I will say certain things to each one of them that I wouldn’t say to the rest of the world, and that’s why I can’t tell you much more than that,” Trump said in a March interview with former aide Sebastian Gorka.

His public silence on his negotiating tack has left room for others to fill in the blanks. Hungarian Prime Minister Viktor Orban, who has antagonized European allies with his autocratic and pro-Russian tendencies, met with Trump last month and afterward claimed Trump told him he will force the war to end because “he will not give a penny” to help Ukraine. Orban’s statement was false, but the former president didn’t want to publicly contradict him after entertaining him all night at his Mar-a-Lago Club and admiring his toughness and anti-immigration positions, according to a person close to Trump, who spoke on the condition of anonymity to describe a private conversation.

During the meeting, Orban spoke at length about Soviet history, Russia’s desire for Ukrainian territory and the military challenges facing Ukraine, the person said. Trump listened but was noncommittal, the person said. An Orban spokesman did not respond to a request for comment.

Word of Trump’s plan for Ukraine circulated in Washington last November at a meeting at the Heritage Foundation between right-of-center foreign policy figures and a visiting delegation from the European Council on Foreign Relations. Former Trump White House aide Michael Anton described the expected contours of Trump’s peace plan as Ukraine ceding territory in Crimea and Donbas, limiting NATO expansion and enticing Putin to loosen his growing reliance on China, according to multiple people present for the meeting, who like others spoke on the condition of anonymity to describe a private discussion.

Reached by phone in March, Anton said he hadn’t spoken with Trump in 18 to 24 months and denied knowing anything about Trump’s plan for Ukraine. He did not respond to further questions.

James Carafano, a Heritage Foundation fellow who convened the meeting, declined to comment on the private discussion but criticized the idea of splitting Russia from China. “That is stupid idea 101,” he said. “Anything you could give Russia that they would really value would compromise all your other interests. The way to deal with the Russia-China relationship is to make Russia a weaker partner.”

Peeling Russia away from China would presumably involve sanctions relief, since the Kremlin has turned toward Beijing to try to offset broad-based Western sanctions on its energy, defense and financial sectors, said Jeremy Shapiro, head of the Washington office of the European Council on Foreign Relations, who brought the group’s delegation to the meeting in November. Shapiro declined to comment on the specifics of the conversation, citing ground rules of the November event that prohibited attributing anything that was said, but he said that Trump’s Ukraine peace plan did not appear to be detailed.

“Trump people feel as if one of the great sins of the Ukrainian war and the Russia policy, generally speaking, is to push Russia toward China and to make it all the more dependent on China,” he said. Trump’s “fundamental approach with all things is to get men in a room together to discuss,” without necessarily having detailed plans in advance, Shapiro said.

Russia experts doubted Trump’s peace efforts could succeed. Fiona Hill, a senior fellow at the Brookings Institution who was Trump’s top Russia adviser and has since emerged as a prominent critic, said it reminded her of 2017 — when unvetted foreigners and business executives approached Trump with various peace plans, and he thought he could sit down with Russia and Ukraine and mediate on the strength of his personal charisma.

Trump’s team “is thinking about this very much in silos, that this is just a Ukraine-Russia thing,” Hill said. “They think of it as a territorial dispute, rather than one about the whole future of European security and the world order by extension.”

Even drawing an armistice line might not be so straightforward. The Kremlin in September 2022 declared that it was annexing four southern and eastern Ukrainian provinces, including the Donbas region but extending well beyond it. Since Kyiv still controls much of the territory, any attempt to resolve the war with territorial concessions is likely to involve extensive haggling — unless both sides simply agree to freeze the front lines that are in place at the moment of a deal.

Ukraine and European allies would probably resist Trump’s efforts to strike a deal with Moscow, Hill said. She added that the United States has limited leverage for a unilateral deal because meaningful sanctions relief would rely on European cooperation.

“No amount of leverage the United States has is likely to compel Ukrainian leadership to engage in policies that would constitute domestic political suicide,” said Michael Kofman, an analyst of the Russia-Ukraine war at the Carnegie Endowment for International Peace, a nonpartisan research center. “And no amount of leverage the United States has can compel Ukraine to cede territory or engage in these types of concessions. This is a situation where if you’re willing to give a hand, the other side will very quickly want the rest of the arm.”

Election 2024

Get the latest news on the 2024 election from our reporters on the campaign trail and in Washington.

Who is running? President Biden and Donald Trump secured their parties’ nominations for the presidency , formalizing a general-election rematch.

Key dates and events: From January to June, voters in all states and U.S. territories will pick their party’s nominee for president ahead of the summer conventions. Here are key dates and events on the 2024 election calendar .

Abortion and the election: Voters in a dozen states in this pivotal election year could decide the fate of abortion rights with constitutional amendments on the ballot. Biden supports legal access to abortion , and he has encouraged Congress to pass a law that would codify abortion rights nationwide. After months of mixed signals about his position, Trump said the issue should be left to states . Here’s how Trump’s abortion stance has shifted over the years.

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